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Well since we know \[\large P = \frac{W}{\Delta t}\] And we know Work is a force over some distance we have \[\large P = \frac{Fx}{\Delta t}\] Now think about the fact that a distance, over a change in time...sounds just like the velocity *speed* of an object doesnt it? so we have the alternative definition for power as \[\large P = F\vec{v}\]
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